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Problem: Fit second degree parabola equation {{1996,1997,1998,1999,2000},{40,50,62,58,60}} [ Calculator, Method and examples ]

Solution:
Your problem -> Fit second degree parabola equation {{1996,1997,1998,1999,2000},{40,50,62,58,60}}

The equation is y = a + bx + cx^2 and the normal equations are

sum y = an + b sum x + c sum x^2

sum xy = a sum x + b sum x^2 + c sum x^3

sum x^2y = a sum x^2 + b sum x^3 + c sum x^4

 X y x = X - 1998 x^2 x^3 x^4 x*y x^2*y 1996 40 -2 4 -8 16 -80 160 1997 50 -1 1 -1 1 -50 50 1998 62 0 0 0 0 0 0 1999 58 1 1 1 1 58 58 2000 60 2 4 8 16 120 240 --- --- --- --- --- --- --- --- 9990 270 0 10 0 34 48 508

Substituting these values in the normal equations
270=5a+0b+10c

48=0a+10b+0c

508=10a+0b+34c

Solving these 3 equations,
Total Equations are 3

5a+0b+10c=270 -> (1)

0a+10b+0c=48 -> (2)

10a+0b+34c=508 -> (3)

Select the equations (1) and (3), and eliminate the variable a.

 5a+10c=270  xx 2->  10a + 20c = 540  − 10a+34c=508  xx 1->  10a + 34c = 508  - 14c = 32  -> (4)

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